TSTP Solution File: FLD067-2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : FLD067-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n010.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Aug 22 10:37:40 EDT 2023

% Result   : Unsatisfiable 153.67s 137.26s
% Output   : CNFRefutation 153.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   99 (  36 unt;  12 typ;   0 def)
%            Number of atoms       :  173 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  182 (  96   ~;  86   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   7   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   81 (;  81   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ less_or_equal > equalish > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > u > multiplicative_identity > b > additive_identity > a

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(less_or_equal,type,
    less_or_equal: ( $i * $i ) > $o ).

tff(a,type,
    a: $i ).

tff(additive_identity,type,
    additive_identity: $i ).

tff(multiplicative_identity,type,
    multiplicative_identity: $i ).

tff(u,type,
    u: $i ).

tff(multiply,type,
    multiply: ( $i * $i ) > $i ).

tff(additive_inverse,type,
    additive_inverse: $i > $i ).

tff(b,type,
    b: $i ).

tff(defined,type,
    defined: $i > $o ).

tff(multiplicative_inverse,type,
    multiplicative_inverse: $i > $i ).

tff(add,type,
    add: ( $i * $i ) > $i ).

tff(equalish,type,
    equalish: ( $i * $i ) > $o ).

tff(f_238,axiom,
    defined(u),
    file(unknown,unknown) ).

tff(f_173,axiom,
    ! [X,Y] :
      ( less_or_equal(X,Y)
      | less_or_equal(Y,X)
      | ~ defined(X)
      | ~ defined(Y) ),
    file(unknown,unknown) ).

tff(f_126,axiom,
    defined(additive_identity),
    file(unknown,unknown) ).

tff(f_131,axiom,
    ! [X] :
      ( defined(additive_inverse(X))
      | ~ defined(X) ),
    file(unknown,unknown) ).

tff(f_67,axiom,
    ! [X] :
      ( equalish(add(X,additive_inverse(X)),additive_identity)
      | ~ defined(X) ),
    file(unknown,unknown) ).

tff(f_199,axiom,
    ! [X,Y] :
      ( equalish(X,Y)
      | ~ equalish(Y,X) ),
    file(unknown,unknown) ).

tff(f_62,axiom,
    ! [X] :
      ( equalish(add(additive_identity,X),X)
      | ~ defined(X) ),
    file(unknown,unknown) ).

tff(f_207,axiom,
    ! [X,Z,Y] :
      ( equalish(X,Z)
      | ~ equalish(X,Y)
      | ~ equalish(Y,Z) ),
    file(unknown,unknown) ).

tff(f_231,axiom,
    ! [Y,Z,X] :
      ( less_or_equal(Y,Z)
      | ~ less_or_equal(X,Z)
      | ~ equalish(X,Y) ),
    file(unknown,unknown) ).

tff(f_242,axiom,
    ~ less_or_equal(additive_identity,u),
    file(unknown,unknown) ).

tff(f_236,axiom,
    defined(a),
    file(unknown,unknown) ).

tff(f_237,axiom,
    defined(b),
    file(unknown,unknown) ).

tff(f_75,axiom,
    ! [X,Y] :
      ( equalish(add(X,Y),add(Y,X))
      | ~ defined(X)
      | ~ defined(Y) ),
    file(unknown,unknown) ).

tff(f_240,axiom,
    equalish(add(b,additive_inverse(a)),u),
    file(unknown,unknown) ).

tff(f_239,axiom,
    less_or_equal(a,b),
    file(unknown,unknown) ).

tff(f_181,axiom,
    ! [X,Z,Y] :
      ( less_or_equal(add(X,Z),add(Y,Z))
      | ~ defined(Z)
      | ~ less_or_equal(X,Y) ),
    file(unknown,unknown) ).

tff(f_189,axiom,
    ! [Y,Z] :
      ( less_or_equal(additive_identity,multiply(Y,Z))
      | ~ less_or_equal(additive_identity,Y)
      | ~ less_or_equal(additive_identity,Z) ),
    file(unknown,unknown) ).

tff(f_163,axiom,
    ! [X,Z,Y] :
      ( less_or_equal(X,Z)
      | ~ less_or_equal(X,Y)
      | ~ less_or_equal(Y,Z) ),
    file(unknown,unknown) ).

tff(f_155,axiom,
    ! [X,Y] :
      ( equalish(X,Y)
      | ~ less_or_equal(X,Y)
      | ~ less_or_equal(Y,X) ),
    file(unknown,unknown) ).

tff(c_60,plain,
    defined(u),
    inference(cnfTransformation,[status(thm)],[f_238]) ).

tff(c_36,plain,
    ! [Y_30,X_29] :
      ( ~ defined(Y_30)
      | ~ defined(X_29)
      | less_or_equal(Y_30,X_29)
      | less_or_equal(X_29,Y_30) ),
    inference(cnfTransformation,[status(thm)],[f_173]) ).

tff(c_191,plain,
    ! [Y_30] :
      ( ~ defined(Y_30)
      | less_or_equal(Y_30,Y_30) ),
    inference(factorization,[status(thm),theory(equality)],[c_36]) ).

tff(c_22,plain,
    defined(additive_identity),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_24,plain,
    ! [X_20] :
      ( ~ defined(X_20)
      | defined(additive_inverse(X_20)) ),
    inference(cnfTransformation,[status(thm)],[f_131]) ).

tff(c_99,plain,
    ! [X_64] :
      ( ~ defined(X_64)
      | equalish(add(X_64,additive_inverse(X_64)),additive_identity) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_44,plain,
    ! [Y_38,X_37] :
      ( ~ equalish(Y_38,X_37)
      | equalish(X_37,Y_38) ),
    inference(cnfTransformation,[status(thm)],[f_199]) ).

tff(c_102,plain,
    ! [X_64] :
      ( equalish(additive_identity,add(X_64,additive_inverse(X_64)))
      | ~ defined(X_64) ),
    inference(resolution,[status(thm)],[c_99,c_44]) ).

tff(c_4,plain,
    ! [X_4] :
      ( ~ defined(X_4)
      | equalish(add(additive_identity,X_4),X_4) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_107,plain,
    ! [Y_66,Z_67,X_68] :
      ( ~ equalish(Y_66,Z_67)
      | ~ equalish(X_68,Y_66)
      | equalish(X_68,Z_67) ),
    inference(cnfTransformation,[status(thm)],[f_207]) ).

tff(c_1247,plain,
    ! [X_136,X_137] :
      ( ~ equalish(X_136,add(additive_identity,X_137))
      | equalish(X_136,X_137)
      | ~ defined(X_137) ),
    inference(resolution,[status(thm)],[c_4,c_107]) ).

tff(c_1271,plain,
    ( equalish(additive_identity,additive_inverse(additive_identity))
    | ~ defined(additive_inverse(additive_identity))
    | ~ defined(additive_identity) ),
    inference(resolution,[status(thm)],[c_102,c_1247]) ).

tff(c_1298,plain,
    ( equalish(additive_identity,additive_inverse(additive_identity))
    | ~ defined(additive_inverse(additive_identity)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_1271]) ).

tff(c_1334,plain,
    ~ defined(additive_inverse(additive_identity)),
    inference(splitLeft,[status(thm)],[c_1298]) ).

tff(c_1337,plain,
    ~ defined(additive_identity),
    inference(resolution,[status(thm)],[c_24,c_1334]) ).

tff(c_1341,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_1337]) ).

tff(c_1342,plain,
    equalish(additive_identity,additive_inverse(additive_identity)),
    inference(splitRight,[status(thm)],[c_1298]) ).

tff(c_46,plain,
    ! [Y_41,Z_40,X_39] :
      ( ~ equalish(Y_41,Z_40)
      | ~ equalish(X_39,Y_41)
      | equalish(X_39,Z_40) ),
    inference(cnfTransformation,[status(thm)],[f_207]) ).

tff(c_1447,plain,
    ! [X_143] :
      ( ~ equalish(X_143,additive_identity)
      | equalish(X_143,additive_inverse(additive_identity)) ),
    inference(resolution,[status(thm)],[c_1342,c_46]) ).

tff(c_52,plain,
    ! [X_50,Y_48,Z_49] :
      ( ~ equalish(X_50,Y_48)
      | ~ less_or_equal(X_50,Z_49)
      | less_or_equal(Y_48,Z_49) ),
    inference(cnfTransformation,[status(thm)],[f_231]) ).

tff(c_29263,plain,
    ! [X_516,Z_517] :
      ( ~ less_or_equal(X_516,Z_517)
      | less_or_equal(additive_inverse(additive_identity),Z_517)
      | ~ equalish(X_516,additive_identity) ),
    inference(resolution,[status(thm)],[c_1447,c_52]) ).

tff(c_31117,plain,
    ! [Y_526] :
      ( less_or_equal(additive_inverse(additive_identity),Y_526)
      | ~ equalish(Y_526,additive_identity)
      | ~ defined(Y_526) ),
    inference(resolution,[status(thm)],[c_191,c_29263]) ).

tff(c_1379,plain,
    equalish(additive_inverse(additive_identity),additive_identity),
    inference(resolution,[status(thm)],[c_1342,c_44]) ).

tff(c_1386,plain,
    ! [Z_49] :
      ( ~ less_or_equal(additive_inverse(additive_identity),Z_49)
      | less_or_equal(additive_identity,Z_49) ),
    inference(resolution,[status(thm)],[c_1379,c_52]) ).

tff(c_31414,plain,
    ! [Y_528] :
      ( less_or_equal(additive_identity,Y_528)
      | ~ equalish(Y_528,additive_identity)
      | ~ defined(Y_528) ),
    inference(resolution,[status(thm)],[c_31117,c_1386]) ).

tff(c_66,plain,
    ~ less_or_equal(additive_identity,u),
    inference(cnfTransformation,[status(thm)],[f_242]) ).

tff(c_31455,plain,
    ( ~ equalish(u,additive_identity)
    | ~ defined(u) ),
    inference(resolution,[status(thm)],[c_31414,c_66]) ).

tff(c_31487,plain,
    ~ equalish(u,additive_identity),
    inference(demodulation,[status(thm),theory(equality)],[c_60,c_31455]) ).

tff(c_56,plain,
    defined(a),
    inference(cnfTransformation,[status(thm)],[f_236]) ).

tff(c_58,plain,
    defined(b),
    inference(cnfTransformation,[status(thm)],[f_237]) ).

tff(c_435,plain,
    ! [Y_93,X_94] :
      ( ~ defined(Y_93)
      | ~ defined(X_94)
      | equalish(add(X_94,Y_93),add(Y_93,X_94)) ),
    inference(cnfTransformation,[status(thm)],[f_75]) ).

tff(c_64,plain,
    equalish(add(b,additive_inverse(a)),u),
    inference(cnfTransformation,[status(thm)],[f_240]) ).

tff(c_133,plain,
    ! [X_68] :
      ( ~ equalish(X_68,add(b,additive_inverse(a)))
      | equalish(X_68,u) ),
    inference(resolution,[status(thm)],[c_64,c_107]) ).

tff(c_439,plain,
    ( equalish(add(additive_inverse(a),b),u)
    | ~ defined(b)
    | ~ defined(additive_inverse(a)) ),
    inference(resolution,[status(thm)],[c_435,c_133]) ).

tff(c_448,plain,
    ( equalish(add(additive_inverse(a),b),u)
    | ~ defined(additive_inverse(a)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_58,c_439]) ).

tff(c_499,plain,
    ~ defined(additive_inverse(a)),
    inference(splitLeft,[status(thm)],[c_448]) ).

tff(c_502,plain,
    ~ defined(a),
    inference(resolution,[status(thm)],[c_24,c_499]) ).

tff(c_506,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_56,c_502]) ).

tff(c_508,plain,
    defined(additive_inverse(a)),
    inference(splitRight,[status(thm)],[c_448]) ).

tff(c_62,plain,
    less_or_equal(a,b),
    inference(cnfTransformation,[status(thm)],[f_239]) ).

tff(c_38,plain,
    ! [X_31,Y_33,Z_32] :
      ( ~ less_or_equal(X_31,Y_33)
      | ~ defined(Z_32)
      | less_or_equal(add(X_31,Z_32),add(Y_33,Z_32)) ),
    inference(cnfTransformation,[status(thm)],[f_181]) ).

tff(c_6,plain,
    ! [X_5] :
      ( ~ defined(X_5)
      | equalish(add(X_5,additive_inverse(X_5)),additive_identity) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_135,plain,
    ! [X_69,Y_70,Z_71] :
      ( ~ equalish(X_69,Y_70)
      | ~ less_or_equal(X_69,Z_71)
      | less_or_equal(Y_70,Z_71) ),
    inference(cnfTransformation,[status(thm)],[f_231]) ).

tff(c_2209,plain,
    ! [X_158,Z_159] :
      ( ~ less_or_equal(add(X_158,additive_inverse(X_158)),Z_159)
      | less_or_equal(additive_identity,Z_159)
      | ~ defined(X_158) ),
    inference(resolution,[status(thm)],[c_6,c_135]) ).

tff(c_2260,plain,
    ! [Y_33,X_31] :
      ( less_or_equal(additive_identity,add(Y_33,additive_inverse(X_31)))
      | ~ defined(X_31)
      | ~ less_or_equal(X_31,Y_33)
      | ~ defined(additive_inverse(X_31)) ),
    inference(resolution,[status(thm)],[c_38,c_2209]) ).

tff(c_69,plain,
    ! [Y_53,X_54] :
      ( ~ equalish(Y_53,X_54)
      | equalish(X_54,Y_53) ),
    inference(cnfTransformation,[status(thm)],[f_199]) ).

tff(c_74,plain,
    equalish(u,add(b,additive_inverse(a))),
    inference(resolution,[status(thm)],[c_64,c_69]) ).

tff(c_160,plain,
    ! [Z_71] :
      ( ~ less_or_equal(u,Z_71)
      | less_or_equal(add(b,additive_inverse(a)),Z_71) ),
    inference(resolution,[status(thm)],[c_74,c_135]) ).

tff(c_319,plain,
    ! [Z_86,Y_87] :
      ( ~ less_or_equal(additive_identity,Z_86)
      | ~ less_or_equal(additive_identity,Y_87)
      | less_or_equal(additive_identity,multiply(Y_87,Z_86)) ),
    inference(cnfTransformation,[status(thm)],[f_189]) ).

tff(c_34,plain,
    ! [Y_28,Z_27,X_26] :
      ( ~ less_or_equal(Y_28,Z_27)
      | ~ less_or_equal(X_26,Y_28)
      | less_or_equal(X_26,Z_27) ),
    inference(cnfTransformation,[status(thm)],[f_163]) ).

tff(c_5712,plain,
    ! [X_235,Y_236,Z_237] :
      ( ~ less_or_equal(X_235,additive_identity)
      | less_or_equal(X_235,multiply(Y_236,Z_237))
      | ~ less_or_equal(additive_identity,Z_237)
      | ~ less_or_equal(additive_identity,Y_236) ),
    inference(resolution,[status(thm)],[c_319,c_34]) ).

tff(c_161,plain,
    ! [Z_71] :
      ( ~ less_or_equal(add(b,additive_inverse(a)),Z_71)
      | less_or_equal(u,Z_71) ),
    inference(resolution,[status(thm)],[c_64,c_135]) ).

tff(c_5810,plain,
    ! [Y_236,Z_237] :
      ( less_or_equal(u,multiply(Y_236,Z_237))
      | ~ less_or_equal(add(b,additive_inverse(a)),additive_identity)
      | ~ less_or_equal(additive_identity,Z_237)
      | ~ less_or_equal(additive_identity,Y_236) ),
    inference(resolution,[status(thm)],[c_5712,c_161]) ).

tff(c_277320,plain,
    ~ less_or_equal(add(b,additive_inverse(a)),additive_identity),
    inference(splitLeft,[status(thm)],[c_5810]) ).

tff(c_277376,plain,
    ~ less_or_equal(u,additive_identity),
    inference(resolution,[status(thm)],[c_160,c_277320]) ).

tff(c_277409,plain,
    ( ~ defined(u)
    | ~ defined(additive_identity)
    | less_or_equal(additive_identity,u) ),
    inference(resolution,[status(thm)],[c_36,c_277376]) ).

tff(c_277437,plain,
    less_or_equal(additive_identity,u),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_60,c_277409]) ).

tff(c_277439,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_66,c_277437]) ).

tff(c_277441,plain,
    less_or_equal(add(b,additive_inverse(a)),additive_identity),
    inference(splitRight,[status(thm)],[c_5810]) ).

tff(c_32,plain,
    ! [Y_25,X_24] :
      ( ~ less_or_equal(Y_25,X_24)
      | ~ less_or_equal(X_24,Y_25)
      | equalish(X_24,Y_25) ),
    inference(cnfTransformation,[status(thm)],[f_155]) ).

tff(c_277497,plain,
    ( ~ less_or_equal(additive_identity,add(b,additive_inverse(a)))
    | equalish(additive_identity,add(b,additive_inverse(a))) ),
    inference(resolution,[status(thm)],[c_277441,c_32]) ).

tff(c_403163,plain,
    ~ less_or_equal(additive_identity,add(b,additive_inverse(a))),
    inference(splitLeft,[status(thm)],[c_277497]) ).

tff(c_403183,plain,
    ( ~ defined(a)
    | ~ less_or_equal(a,b)
    | ~ defined(additive_inverse(a)) ),
    inference(resolution,[status(thm)],[c_2260,c_403163]) ).

tff(c_403203,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_508,c_62,c_56,c_403183]) ).

tff(c_403204,plain,
    equalish(additive_identity,add(b,additive_inverse(a))),
    inference(splitRight,[status(thm)],[c_277497]) ).

tff(c_403277,plain,
    equalish(additive_identity,u),
    inference(resolution,[status(thm)],[c_403204,c_133]) ).

tff(c_403316,plain,
    equalish(u,additive_identity),
    inference(resolution,[status(thm)],[c_403277,c_44]) ).

tff(c_403339,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_31487,c_403316]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : FLD067-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35  % Computer : n010.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 19:45:13 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 153.67/137.26  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 153.67/137.27  
% 153.67/137.27  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 153.67/137.31  
% 153.67/137.31  Inference rules
% 153.67/137.31  ----------------------
% 153.67/137.31  #Ref     : 0
% 153.67/137.31  #Sup     : 87937
% 153.67/137.31  #Fact    : 30
% 153.67/137.31  #Define  : 0
% 153.67/137.31  #Split   : 97
% 153.67/137.31  #Chain   : 0
% 153.67/137.31  #Close   : 0
% 153.67/137.31  
% 153.67/137.31  Ordering : KBO
% 153.67/137.31  
% 153.67/137.31  Simplification rules
% 153.67/137.31  ----------------------
% 153.67/137.31  #Subsume      : 23050
% 153.67/137.31  #Demod        : 49689
% 153.67/137.31  #Tautology    : 14491
% 153.67/137.31  #SimpNegUnit  : 2112
% 153.67/137.31  #BackRed      : 0
% 153.67/137.31  
% 153.67/137.31  #Partial instantiations: 0
% 153.67/137.31  #Strategies tried      : 1
% 153.67/137.31  
% 153.67/137.31  Timing (in seconds)
% 153.67/137.31  ----------------------
% 153.67/137.31  Preprocessing        : 0.50
% 153.67/137.31  Parsing              : 0.28
% 153.67/137.31  CNF conversion       : 0.03
% 153.67/137.31  Main loop            : 135.65
% 153.67/137.31  Inferencing          : 10.67
% 153.67/137.31  Reduction            : 64.21
% 153.67/137.31  Demodulation         : 52.53
% 153.67/137.31  BG Simplification    : 0.35
% 153.67/137.31  Subsumption          : 48.06
% 153.67/137.31  Abstraction          : 0.66
% 153.67/137.31  MUC search           : 0.00
% 153.67/137.31  Cooper               : 0.00
% 153.67/137.31  Total                : 136.22
% 153.67/137.31  Index Insertion      : 0.00
% 153.67/137.31  Index Deletion       : 0.00
% 153.67/137.31  Index Matching       : 0.00
% 153.67/137.31  BG Taut test         : 0.00
%------------------------------------------------------------------------------